Norm equalities for operators on Banach spaces Vladimir KadetsMircea MartinJavier Meri 46B2047A99Daugavet equationoperator norm A Banach space $X$ has the Daugavet property if the Daugavet equation $\| \mathrm{Id} + T \| = 1 + \| T \|$ holds for every rank-one operator $T : X \to X$. We show that the most natural attempts to introduce new properties by considering other norm equalities for operators (like $\| g(T) \| = f(\| T \|)$ for some functions $f$ and $g$) lead in fact to the Daugavet property of the space. On the other hand, there are equations (for example $\| \mathrm{Id} + T \| = \| \mathrm{Id} - T \|$) that lead to new, strictly weaker properties of Banach spaces. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3046 10.1512/iumj.2007.56.3046 en Indiana Univ. Math. J. 56 (2007) 2385 - 2412 state-of-the-art mathematics http://iumj.org/access/